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3 years ago

Pls help me and show working

Mathematics

1 answer:

Juliette [100K]3 years ago

6 0

Answer:

4x + 10 > 3x + 14

x > 4

Step-by-step explanation:

Use the given values for length and width in the formula for perimeter of a rectangle. You will be able to find the perimeter of rectangles A and B.

A = 2(l + w)

A = 2(x + 5 + x)

A = 2(2x + 5)

A = 4x + 10

B = 2(l + w)

B = 2(x + 7 + x/2)

B = 2(3x/2 + 7)

B = 3x + 14

The perimeter of rectangle A is larger than that of rectangle B.

A > B

4x + 10 > 3x + 14

(4x + 10) - 3x > (3x + 14) - 3x

x + 10 > 14

(x + 10) - 10 > 14 - 10

x > 4

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Stu trained for a triathlon for 5 hours yesterday. He ran 5 miles and then biked 80 miles. His biking speed is 15 mph faster tha

lara31 [8.8K]

Answer:

Step-by-step explanation:

Given as :

The distance cover while running = $D_1$ = 5 miles

Let The speed for running = $S_1$

The distance cover with bike = $D_2$ = 80 miles

The speed for biking = $S_2$ = 15 mph + $S_1$

Total Time taken = 5 hours

Now Time = $\dfrac{\textrm Distance}{\textrm Speed}$

∴ 5 hour = $\frac{D_1}{S_1}$ + $\frac{D_2}{S_2}$

Or, 5 hour = $\frac{5}{S_1}$ + $\frac{80}{15+S_1}$

Or, 5 hour = $\frac{75 + 5 S_1 + 80 S_1}{S_1(15+S_1)}$

or, 5 × ( $S_1^{2}+15 S_1$ ) = $85 S_1 + 75$

Or, $5 S_1^{2} + 75 S_1$ - $85 S_1 - 75$ = 0

or, $5 S_1^{2} -10 S_1 - 75$ = 0

or, $S_1^{2} -2 S_1 - 15$ = 0

Or, $S_1^{2} -3 S_1 + 5 S_1- 15$ = 0

Or, $S_1 (S_1 - 3) + 5 (S_1 - 3)$ = 0

Or, $(S_1 - 3) ( S_1 + 5 )$ = 0

∴ $S_1$ = 3 , - 5

So, the running speed = 3 mile per hour

And the biking speed = 15 mph + 3 mph = 18 mile per hour

Hence The running speed of Stu is 3 mile per hour . Answer

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3 years ago

Austin has $5 more than Mark. If Mark has Δ dollars, write an expression for the amount of money Austin has.

elixir [45]

Mark+5=austin
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3 years ago

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rusak2 [61]

Answer:

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Step-by-step explanation

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2 years ago

Give that 5x=3(mod7)find x

pychu [463]

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2 years ago

Factor the polynomial, x2 + 5x + 6

patriot [66]

Answer:

Choice b.

$x^{2} + 5\, x + 6 = (x + 3)\, (x + 2)$ .

Step-by-step explanation:

The highest power of the variable $x$ in this polynomial is $2$ . In other words, this polynomial is quadratic.

It is thus possible to apply the quadratic formula to find the "roots" of this polynomial. (A root of a polynomial is a value of the variable that would set the polynomial to $0$ .)

After finding these roots, it would be possible to factorize this polynomial using the Factor Theorem.

Apply the quadratic formula to find the two roots that would set this quadratic polynomial to $0$ . The discriminant of this polynomial is $(5^{2} - 4 \times 1 \times 6) = 1$ .

$\begin{aligned}x_{1} &= \frac{-5 + \sqrt{1}}{2\times 1} \\ &= \frac{-5 + 1}{2} \\ &= -2\end{aligned}$ .

Similarly:

$\begin{aligned}x_{2} &= \frac{-5 - \sqrt{1}}{2\times 1} \\ &= \frac{-5 - 1}{2} \\ &= -3\end{aligned}$ .

By the Factor Theorem, if $x = x_{0}$ is a root of a polynomial, then $(x - x_0)$ would be a factor of that polynomial. Note the minus sign between $x$ and $x_{0}$ .

The root $x = -2$ corresponds to the factor $(x - (-2))$ , which simplifies to $(x + 2)$ .
The root $x = -3$ corresponds to the factor $(x - (-3))$ , which simplifies to $(x + 3)$ .

Verify that $(x + 2)\, (x + 3)$ indeed expands to the original polynomial:

$\begin{aligned}& (x + 2)\, (x + 3) \\ =\; & x^{2} + 2\, x + 3\, x + 6 \\ =\; & x^{2} + 5\, x + 6\end{aligned}$ .

4 0

2 years ago

Pls help me and show working​

Pls help me and show working